Question

Rent and other associated housing costs, such as utilities, are an important part of the estimated costs of attendance at college. A group of researchers at the BYU Off-Campus Housing department want to estimate the mean monthly rent that unmarried BYU students paid during winter 2018. During March 2018, they randomly sampled 314 BYU students and found that on average, students paid $346 for rent with a standard deviation of $86. The plot of the sample data showed no extreme skewness or outliers. Calculate a 96% confidence interval estimate for the mean monthly rent of all unmarried BYU students in winter 2018.

Answer 1

Answer: $(336.49,\ 355.51)$

Step-by-step explanation:

The confidence interval for population mean is given by :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

Given : Sample size : $n= 314$ , which is a large sample , so we apply z-test .

Sample mean : $\overline{x}=346$

Standard deviation : $\sigma= 86$

Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}=1.96$

Now, a confidence interval at the 95% level of confidence will be :-

$346\pm(1.96)\dfrac{86}{\sqrt{314}}\\\\\approx346\pm9.51\\\\=(346-9.51,\ 346+9.51)\\\\=(336.49,\ 355.51)$